The square root of 1225 is a number whose product with itself results in 1225. The mathematical operation square root is the inverse of square. The square root of a number can be positive or negative, rational or irrational, real or imaginary. In this mini-lesson, we will calculate the square root of 1225 using different methods and will look at some interesting problems related to it.

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Square root of 1225: 35Square of 1225: 1500625
1.What Is the Square Root of 1225?
2.Is Square Root of 1225 Rational or Irrational?
3.How to Find the Square Root of 1225?
4.Important Notes on Square Root of 1225
5.FAQs on Square Root of 1225

What Is the Square Root of 1225?


1225 = a × a = 352Then a = √1225 = √(35× 35)35× 35= 1225 or -35 × -35 = 1225The 2nd root of 1225 is +35 or -35.This shows that 1225 is a perfect square.

Is Square Root of 1225 Rational or Irrational?


A rational number is defined as a number that can be written in the ratio of two integers, that is, p/q where q ≠ 0.35 and -35 can be written as 35/1 and -35/1.Both numbers can be represented in the form of rational numbers.

How to Find the Square Root of 1225?


The square of 1225 can be calculated using the prime factorization method, long division method, or repeated subtraction method.

Square Root of 1225 by Repeated Subtraction Method

Sr. No.

Subtraction

12

1104 - 23 = 1081

24

696 - 47 = 649

1

1225 - 1 = 1224

13

1081 - 25 = 1056

25

649 - 49 = 600

2

1224 - 3 = 1221

14

1056 - 27 = 1029

26

600 - 51 = 549

3

1221 - 5 = 1216

15

1029 - 29 = 1000

27

549 - 53 = 496

4

1216 - 7 = 1209

16

1000 - 31 = 969

28

496 - 55 = 441

5

1209 - 9 = 1200

17

969 - 33 = 936

29

441 - 57 = 384

6

1200 - 11 = 1189

18

936 - 35 = 901

30

384 - 59 = 325

7

1189 - 13 = 1176

19

901 - 37 = 864

31

325 - 61 = 264

8

1176 - 15 = 1161

20

864 - 39 = 825

32

264 - 63 = 201

9

1161 - 17 = 1144

21

825 - 41 = 784

33

201 - 65 = 136

10

1144 - 19 = 1125

22

784 - 43 = 741

34

136 - 67 = 69

11

1125 - 21 = 1104

23

741 - 45 = 696

35

69 - 69 = 0

So, starting from 1225, we have subtracted 35 times to get 0.Thus the square root of 1225 is 35.

Square Root of 1225 by Long Division Method

Follow the steps shown below to find the square root of 1225 by the long division method:

Step 1. Write 1225 as shown in the figure. Pair the number in pairs from the right end by putting a bar on top of them. In the case of 1225, 25 and 12 are the two pairs starting from the right.Step 2. Find a number such that when it is multiplied by itself it results in a number equal to or less than 12. Here the number is 3.

So, the square root of 1225 by the long division method is 35.

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Explore square roots using illustrations and interactive examples.


Important Notes:

The square root of 1225 is represented as √1225 in radical form.The square root of 1225 is represented as (1225)1/2 in exponential form.There will be n/2 digits in the square root of an even number with n digits.There will be (n+2)/2 digits in the square root of an odd number with n digits

Example 1: Paul wants to find the square root of 1225 using the prime factorization method. Can you help Paul?

Solution:The following steps can be followed to find the square root of 1225 using prime factorization:

Step 1. Determine the prime factorization of 12251225 = 5 × 5 × 7 × 71225 = 52 × 72Step 2. Group the prime factors of 1225 in pairs.1225 = 52 × 72Step 3.

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Pick one factor from each pair and the square root of 1225 can be written as:√1225 = √(52 × 72)√1225 = √(5 × 7)2√1225 = ((5 × 7)2)1/2 = ±(5 × 7)√1225 = ±35

Example 2: Ryan is working on a square-shaped table with a surface area of 1225 square inches. He wants to add a protective layer around the sides of the table. The cost of adding a protective layer per inch is given as $0.50. How much will it cost Ryan to add a protective layer around the table?

Solution:The surface area of the square-shaped table = 1225 square inchesLength of one side = √1225 inches = 35 inchesLength of protective layer required = 35 × 4 = 140 inchesCost of adding protective layer = 140 × 0.50 = $70.